The economics of semiconductor fabrication dictates that devices need to be scaled by approximately 70% in linear dimensions every 18-24 months in order to maintain cost effectiveness. Optical lithography has been the driving force for scaling; however, 193 nm immersion lithography approaches its physical resolution limit at about 22 nm. Beyond 22 nm, it is difficult to generate desired patterns using optical lithography. Directed self-assembly (DSA), which combines self-assembling materials and a lithographically defined prepattern, is a potential candidate to extend optical lithography. A lithographically-defined prepattern encoded with spatial chemical and/or topographical information serves to direct the self-assembly process and the pattern formed by the self-assembling materials. The resolution enhancement and self-healing (self-error reduction) effect from DSA are particularly useful to extend the resolution of optical lithography and to rectify the ill-defined patterns printed by optical lithography. For example, the process window of printing via patterns can be increased by employing DSA. To take full advantage of DSA for extending optical lithography requires careful design of the prepattern and the design of the photomask used to form a prepattern on substrates. Such methodologies are currently lacking. Accordingly, there exists a need in the art to mitigate or eliminate the deficiencies and limitations described hereinabove.